Wavelet-based segmentation on the sphere

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational approach and partial differential equation modelling. Wavelets have been used successfully in various problems in image processing, including segmentation, inpainting, noise removal, super-resolution image restoration, and many others. Wavelets on the sphere have been developed to solve such problems for data defined on the sphere, which arise in numerous fields such as cosmology and geophysics. In this work, we propose a wavelet-based method to segment images on the sphere, accounting for the underlying geometry of spherical data. Our method is a direct extension of the tight-frame based segmentation method used to automatically identify tube-like structures such as blood vessels in medical imaging. It is compatible with any arbitrary type of wavelet frame defined on the sphere, such as axisymmetric wavelets, directional wavelets, curvelets, and hybrid wavelet constructions. Such an approach allows the desirable properties of wavelets to be naturally inherited in the segmentation process. In particular, directional wavelets and curvelets, which were designed to efficiently capture directional signal content, provide additional advantages in segmenting images containing prominent directional and curvilinear features. We present several numerical experiments, applying our wavelet-based segmentation method, as well as the common K-means method, on real-world spherical images, including an Earth topographic map, a light probe image, solar data-sets, and spherical retina images. These experiments demonstrate the superiority of our method and show that it is capable of segmenting different kinds of spherical images, including those with prominent directional features. Moreover, our algorithm is efficient with convergence usually within a few iterations.

Curvelets, Image segmentation, Sphere, Tight frame, Wavelets

10.1016/j.patcog.2019.107081

0031-3203

1-15

Cai, Xiaohao

de483445-45e9-4b21-a4e8-b0427fc72cee

Wallis, Christopher G.R.

3e91cdda-348c-426b-9e3b-ad522af106fa

Chan, Jennifer Y.H.

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McEwen, Jason D.

64c6269a-fe40-41d7-8b0c-d3c9ad920175

April 2020

Cai, Xiaohao

de483445-45e9-4b21-a4e8-b0427fc72cee

Wallis, Christopher G.R.

3e91cdda-348c-426b-9e3b-ad522af106fa

Chan, Jennifer Y.H.

c746bb5f-060e-4451-99b6-e801ba2234fe

McEwen, Jason D.

64c6269a-fe40-41d7-8b0c-d3c9ad920175

Cai, Xiaohao, Wallis, Christopher G.R., Chan, Jennifer Y.H. and McEwen, Jason D. (2020) Wavelet-based segmentation on the sphere. Pattern Recognition, 100, 1-15, [107081]. (doi:10.1016/j.patcog.2019.107081).

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Accepted/In Press date: 12 October 2019

e-pub ahead of print date: 4 November 2019

Published date: April 2020

Additional Information: Funding Information: This work is supported by the UK Engineering and Physical Sciences Research Council ( EPSRC ) by grant EP/M011852/1 and EP/M011089/1 . We thank Professor Raymond H. F. Chan in City University, Hong Kong, for the very helpful discussion. We also thank Dr David Peres-Suarez for his help in providing the first set of solar data. We would also like to thank the editors and anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. Xiaohao Cai received his PhD degree in mathematics from The Chinese University of Hong Kong in 2012. He is currently a research fellow in the Mullard Space Science Laboratory at UCL. Before joining UCL, he was a postdoctoral researcher in the Department of Plant Sciences, and Department of Applied Mathematics and Theoretical Physics at the University of Cambridge between 2014 and 2016. His research interests include image/data processing, numerical analysis, inverse problem, and optimisation. Christopher Wallis received his undergraduate masters in physics from Oxford University in 2012 and his PhD in Data analysis in Astrophysics from the University of Manchester in 2015. His research interests are signal processing and machine learning on spherical data sets. Jennifer Y. H. Chan received her Bachelor (Hons.) degree in Physics from the University of Oxford in 2011, and MSc in Astrophysics from the University College London (UCL) in 2013. She is currently a final-year PhD student at the Mullard Space Science Laboratory, UCL. Her interest in sciences finds its root in patterns seen in nature. Her research focuses on probing large-scale cosmic magnetism and reionisation using radio waves, as well as astroinformatics (e.g., all-sky analysis methods, curvelets on the sphere). Jason McEwen is a University Reader (Associate Professor) in the Mullard Space Science Laboratory (MSSL) at University College London (UCL). He is also Director of Research (Astrophysics) of the UCL Centre for Doctoral Training (CDT) in Data Intensive Science (DIS). He completed a PhD at the University of Cambridge in 2007 and has broad multi-disciplinary research interests in applied mathematics, statistics, machine learning, and astrophysics. He is heavily involved in numerous astrophysical experiments, including Planck, Euclid, LSST and the SKA. As part of the Planck team he won the Gruber Prize in Cosmology in 2018. Publisher Copyright: © 2019 Elsevier Ltd

Keywords: Curvelets, Image segmentation, Sphere, Tight frame, Wavelets

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